b) A tensile test was carried out on a mild steel test-piece having a diameter of 12mm and a gauge length of 88mm. During the test, it was found that at the limit of proportionality the load on the test-piece was 41.5kN and the extension of the 88mm gauge length was 0.11mm. It was also found that the maximum load on the specimen during the test was 98KN. Calculate for the steel: a) Its stress at the limit of proportionality. b) Its strain at the limit of proportionality. c) Its Modulus of Elasticity. d) Its Ultimate Tensile Stress.

a) Let R represent the reaction force at Support B. By releasing the beam at Support B and imposing a force R at Point B, the deflection of the beam consists of two parts,i.e. Part I- the deflection caused by MB ; Part II- the deflection caused by R Please treat R, w, h , L , E  as variables in this step , the mathematical equation for the deflection at Point B caused by R ( Part II) can be written as  (Hint : to input equation R2LQ2wh , you can type  (R^2*L)/(Q^2*w*h) )   b) Using the provided data: cross-section width w = 20  mm, cross-section hight h = 93   mm, length of the beam L =3   m , beam material’s Young’s modulus Q =226 GPa, applied bending moment MB = 11 kN.m  The value of the deflection at Point B caused by MB ( Part I) can be calculated as ......(in mm)

Water enters a tank of diameter DT steadily at a mass flow rate of min. An orifice at the bottom with diameter Do allows water to escape. The orifice has a rounded entrance, so the frictional losses are negligible. If the tank is initially empty, (a) determine the maximum height that the water will reach in the tank and (b) obtain a relation for water height z as a function of time?

Question 11) Roger gave the following account of a roller-coaster ride: 1 tried a brand-new ride at a science centre. There's a computer screen that tells you how much the car and the people in it weigh and how high and fast you travel. You get into the car and they strap you in. The car weighs 600 kg. At the top, it moves horizontally at a speed of 1 m/s. Then you drop 30 m, make a loop into the air and finish by riding over an 8-m hill. I don't remember our maximum speed or our speed at the top of the loop, but the ride was fantastic!" Answer the following questions without taking the force of friction into consideration. Show your calculations for each question. A v=1 m/s 20 m 8 m a) What is the highest speed Roger could have attained? What is the potential energy of the roller-coaster car when it is at the top of the b) loop? c) What is the kinetic energy of the car as it passes over the top of the 8 m hill? d) What is the total mechanical energy of the system?